Average Error: 15.1 → 0.4
Time: 28.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}
double f(double r, double a, double b) {
        double r878031 = r;
        double r878032 = b;
        double r878033 = sin(r878032);
        double r878034 = r878031 * r878033;
        double r878035 = a;
        double r878036 = r878035 + r878032;
        double r878037 = cos(r878036);
        double r878038 = r878034 / r878037;
        return r878038;
}
↓
double f(double r, double a, double b) {
        double r878039 = r;
        double r878040 = a;
        double r878041 = cos(r878040);
        double r878042 = b;
        double r878043 = sin(r878042);
        double r878044 = cos(r878042);
        double r878045 = r878043 / r878044;
        double r878046 = r878041 / r878045;
        double r878047 = sin(r878040);
        double r878048 = r878046 - r878047;
        double r878049 = r878039 / r878048;
        return r878049;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.1

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied associate-/l*0.4

    \[\leadsto \color{blue}{\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}}\]

  6. Taylor expanded around inf 0.3

    \[\leadsto \color{blue}{\frac{\sin b \cdot r}{\cos a \cdot \cos b - \sin b \cdot \sin a}}\]

  7. Simplified0.4

    \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}}\]

  8. Final simplification0.4

    \[\leadsto \frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}\]

Reproduce

herbie shell --seed 2019144 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))